login
Numbers that are congruent to {5, 6, 7} mod 8 and are squarefree.
5

%I #20 Sep 08 2022 08:46:17

%S 5,6,7,13,14,15,21,22,23,29,30,31,37,38,39,46,47,53,55,61,62,69,70,71,

%T 77,78,79,85,86,87,93,94,95,101,102,103,109,110,111,118,119,127,133,

%U 134,141,142,143,149,151,157,158,159,165,166,167,173,174

%N Numbers that are congruent to {5, 6, 7} mod 8 and are squarefree.

%C It has been shown, conditional on the Birch Swinnerton-Dyer conjecture, that this sequence is a subset of the primitive congruent numbers (A006991). The union of this sequence with A062695 gives A006991. Also this sequence is the intersection of A047574 and A005117.

%C The asymptotic density of this sequence is 3/Pi^2 (A104141). - _Amiram Eldar_, Mar 09 2021

%H Keith Conrad, <a href="http://www.math.uconn.edu/~kconrad/articles/congruentnumber.pdf">The Congruent Number Problem</a>, The Harvard College Mathematics Review, 2008.

%t Select[Range[1000], MemberQ[{5, 6, 7}, Mod[#, 8]] && SquareFreeQ[#] &]

%o (PARI) is(n) = n % 8 > 4 && issquarefree(n) \\ _Felix Fröhlich_, Jun 04 2016

%o (Magma) [n: n in [1..250] | n mod 8 in [5, 6, 7] and IsSquarefree(n)]; // _Vincenzo Librandi_, Jun 06 2016

%Y Cf. A005117, A006991, A047574, A062695, A104141.

%K nonn

%O 1,1

%A _Frank M Jackson_, Jun 04 2016